easy · Quantitative Finance
An It^o integral of the form I_t = int_0^t H_s dW_s is always a martingale (under standard integrability conditions).
What is the primary reason for this?
- The quadratic variation of the integral is equal to t.
- The integrand H_s must be a deterministic function of time.
- The integrand H_s is adapted, and Brownian increments have zero conditional mean.
- Brownian motion paths have finite variation.
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